计算碳原子系综的能级C

C原子核外6个电子的排布是

轨道的径向部分是

String rj1 ="(z/a0)**(1.5)*2*sympy.exp(-z*r1/a0  )";

String rj2 ="(z/a0)**(1.5)*2*sympy.exp(-z*r2/a0  )";

String rj3="(z/( 2*a1))**(1.5)*(2-z*r1/a1)*sympy.exp(-z*r1/(2*a1)  )";

String rj4="(z/( 2*a1))**(1.5)*(2-z*r2/a1)*sympy.exp(-z*r2/(2*a1)  )";

String rj5="(z/( 2*a1))**(1.5)*(z*r1/(3**0.5*a1) )*sympy.exp(-z*r1/(2*a1)  )";

String rj6="(z/( 2*a1))**(1.5)*(z*r2/(3**0.5*a1) )*sympy.exp(-z*r2/(2*a1)  )";

能级可以展开为

因为

所以

其中E1=-18

E3=-1.96，E5=-1.96。因此动能和势能的和为-43.875Hartrees

设两个P电子的量子数都是（2，1，0）

计算库仑能用公式

计算的J12=3.75，J13=0.36，J15=0.37，J34=0.23，J35=0.24，J56=0.29。库仑排斥能的和为8.19Hartrees

计算交换能用公式

计算的K13=0.06840270133467292，

K15=0.000749325366733499，

K35=0.0439453125，

交换能的和为0.452Hartrees

因此C的能级为

-43.875+8.188502153666878-0.4523893568056257=-36.13 Hartrees

计算程序用前面计算硼原子能级得到的方法，只需将子程序eB（）改为

public static void eC() throws  IOException, ParseException, InterruptedException {
    	

        int z=6;

        int a0=1;
        int a1=4;

        int cn5=0;
        int cn6=0;

        String fx1="(z/a0)**(1.5)*2*sympy.exp(-z*r/a0  )*(4*pi)**(-0.5)";
        String fx2="(z/( 2*a1))**(1.5)*(2-z*r/a1)*sympy.exp(-z*r/(2*a1)  )*(4*pi)**(-0.5)";
        String fx3="(z/( 2*a1))**(1.5)*(z*r/(3**0.5*a1) )*sympy.exp(-z*r/(2*a1)  )*(3/(4*pi))**(0.5)* cos(θ)";


     
        String rj1 ="(z/a0)**(1.5)*2*sympy.exp(-z*r1/a0  )";
        String rj2 ="(z/a0)**(1.5)*2*sympy.exp(-z*r2/a0  )";
 
       String rj3="(z/( 2*a1))**(1.5)*(2-z*r1/a1)*sympy.exp(-z*r1/(2*a1)  )";
       String rj4="(z/( 2*a1))**(1.5)*(2-z*r2/a1)*sympy.exp(-z*r2/(2*a1)  )";
 
       String rj5="(z/( 2*a1))**(1.5)*(z*r1/(3**0.5*a1) )*sympy.exp(-z*r1/(2*a1)  )";
       String rj6="(z/( 2*a1))**(1.5)*(z*r2/(3**0.5*a1) )*sympy.exp(-z*r2/(2*a1)  )";

  
        
          double fh=hin(fx1,fx1)*2+hin(fx2,fx2)*2+hin(fx3,fx3)*2;
          
          double fj=ak( rj1 , rj2 ,0,0,0,0)+ak( rj1 , rj4 ,0,0,0,0)*4+ak( rj1 , rj6 ,0,0,1,cn6)*4+
        	 	    ak( rj3 , rj4 ,0,0,0,0)+ak( rj3 , rj6 ,0,0,1,cn6)*4+ak( rj5 , rj6 ,1,cn5,1,cn6);
          
          double fk=bk( rj1 ,rj4, rj2, rj3,0,0 ,0,0)*4+ bk( rj1 ,rj6, rj2, rj5,0,0 ,1,cn6)*4+
        		    bk( rj3 ,rj6, rj4, rj5,0,0 ,1,cn6)*4;		 
        
        System.out.println( fh+fj-fk +"  "+fh+"  "+fj+"  "+fk +"  "+(fh+fj-fk)*27.2 +"  "+(fh+fj-fk)/37.68 );
          
       
         //System.out.println(  ak( rj5 , rj6 , 1 ,-1 ,1, 1 )  );
       
         }

*徐光宪《量子化学》